A150259 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, 1), (0, 0, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 22, 87, 346, 1427, 6039, 26002, 112859, 495420, 2194216, 9785788, 43863661, 197661583, 894722412, 4065031531, 18527896651, 84707265379, 388318219755, 1784302205549, 8216313095837, 37910019267270, 175232387617041, 811291848163524, 3761807750138514, 17467417679300386, 81212476584580249

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A073075 A299021 A153475 * A165531 A374542 A150260

Adjacent sequences: A150256 A150257 A150258 * A150260 A150261 A150262

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved